This research focuses on solving Kirchhoff-type fractional $p$-Laplacian BVPs with hybrid impulsive effects (instantaneous and non-instantaneous types). Through the use of variational methods, the existence of solutions and multiple solutions for the aforementioned problem are established under assumptions weaker than the super- $p$-linear Ambrosetti-Rabinowitz type growth condition. Finally, an example demonstrates the validity of the paper's main results.

This research focused on solving fractional Sturm-Liouville equations subject to mixed boundary conditions and a combination of instantaneous and non-instantaneous impulses. Through the use of variational methods, the existence of both solutions and multiple solutions for the aforementioned problem was established under assumptions that were weaker than the classical superlinear Ambrosetti-Rabinowitz type growth requirement. Finally, the examples demonstrated the validity of the paper's results.